In the paper, we study numerically the projections of the real exchange rate
dynamics onto the string-like topology. Our approach is inspired by the
contemporary movements in the string theory. The string map of data is defined
here by the boundary conditions, characteristic length, real valued and the
method of redistribution of information. As a practical matter, this map
represents the detrending and data standardization procedure. We introduced
maps onto 1-end-point and 2-end-point open strings that satisfy the Dirichlet
and Neumann boundary conditions. The questions of the choice of
extra-dimensions, symmetries, duality and ways to the partial compactification
are discussed. Subsequently, we pass to higher dimensional and more complex
objects. The 2D-Brane was suggested which incorporated bid-ask spreads.
Polarization by the spread was considered which admitted analyzing arbitrage
opportunities on the market where transaction costs are taken into account. The
model of the rotating string which naturally yields calculation of angular
momentum is suitable for tracking of several currency pairs. The systematic way
which allows one suggest more structured maps suitable for a simultaneous study
of several currency pairs was analyzed by means of the G\^{a}teaux generalized
differential calculus. The effect of the string and brane maps on test data was
studied by comparing their mean statistical characteristics. The study revealed
notable differences between topologies. We review the dependence on the
characteristic string length, mean fluctuations and properties of the
intra-string statistics. The study explores the coupling of the string
amplitude and volatility.Comment: SORS Research a.s, 040 01 Kosice, Slovak Republic, 28 pages, 10
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